{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "from sympy.abc import *\n",
    "from sympy import sin, cos, pi\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "from IPython.display import display, Math\n",
    "from handcalcs import *\n",
    "from sympy.physics.hydrogen import*\n",
    "f,g,T,V,T= symbols('f g x v t', cls=Function)\n",
    "w_0,w_1,w_2,v_0,v_1,J_0,J_1,J_A,J_B,m_1,m_2,J_2,w,phi,w_1,phi_1,w_2,phi_2= symbols('w_0 w_1 w_2 v_0 v_1,J_0,J_1,J_A,J_B,m_1,m_2,J_2,omega,varphi,omega_1,varphi_1,omega_2,varphi_2')\n",
    "x,v_10,v_2,v_20,e=symbols(\"x v_1' v_2 v_2' e\")\n",
    "beta=symbols('beta')\n",
    "def out(x,x_1=0,x_2=0,x_3=0,x_4=0,x_5=0,x_6=0,x_7=0,x_8=0,x_9=0,x_10=0,x_11=0):\n",
    "   if x==0:\n",
    "      return\n",
    "   if x_1==0:\n",
    "       display(Math(latex(x)))\n",
    "   else:\n",
    "       if type(x_1)==str:\n",
    "          display(Math(x_1+latex(x)))\n",
    "       else:\n",
    "           display(Math(latex(x)))\n",
    "   out(x_2,x_3)\n",
    "   out(x_4,x_5)\n",
    "   out(x_6,x_7)\n",
    "   out(x_8,x_9)\n",
    "   out(x_10,x_11)\n",
    "def tex(x):\n",
    "   print(latex(x))\n",
    "def r1(x,y):\n",
    "   return Rational(x,y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# @handcalc(left=\"\",right=\"\",jupyter_display=True)\n",
    "# def NormalDistribution(x, y):\n",
    "#    y=sqrt(y)\n",
    "#    t=sqrt(2*pi)\n",
    "#    m=exp() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# out(factor_list(x**2*z + 4*x*y*z + 4*y**2*z))\n",
    "# out(Integral(m*n,x,x,x,x,x,x))\n",
    "# out(int1(exp(x),x**3+x))\n",
    "# integrate(exp(x)*(x**3+x)) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# @handcalc(left=\"\",right=\"\",jupyter_display=True)\n",
    "def int1(ff, gg,mode=0):\n",
    "  if mode==0:\n",
    "      first=integrate(ff)\n",
    "      second=gg\n",
    "      t=gg\n",
    "      for i in range(100):\n",
    "        t=diff(t)\n",
    "        if t==0:\n",
    "          first=integrate(gg)\n",
    "          second=ff\n",
    "          break\n",
    "      diff_first=first\n",
    "      inter_second=second\n",
    "      ans=0\n",
    "      while(diff_first!=0):\n",
    "          diff_first=diff(diff_first,x)\n",
    "          inter_second=integrate(inter_second,x)\n",
    "          ans=ans+diff_first*inter_second\n",
    "      return ans\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int\\limits_{0}^{1} \\frac{x}{\\sin{\\left(x \\right)}}\\, dx$"
      ],
      "text/plain": [
       "Integral(x/sin(x), (x, 0, 1))"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.vector import *\n",
    "N = CoordSys3D('N')\n",
    "v1 = x/sin(x)\n",
    "integrate(v1,(x,0,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3$"
      ],
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = CoordSys3D('C')\n",
    "f=ParametricRegion((t, t**2), (t, -1, 2))\n",
    "vector_integrate(C.i,f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 8 \\pi$"
      ],
      "text/plain": [
       "8*pi"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "param_circle = ParametricRegion((4*cos(theta), 4*sin(theta)), (theta, 0, 2*pi))\n",
    "vector_integrate(1, param_circle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left[\\begin{matrix}- \\frac{2 \\sqrt{5}}{5}\\\\\\frac{\\sqrt{5}}{5}\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{2 \\sqrt{5}}{15}\\\\\\frac{4 \\sqrt{5}}{15}\\\\\\frac{\\sqrt{5}}{3}\\end{matrix}\\right], \\  \\left[\\begin{matrix}- \\frac{1}{3}\\\\- \\frac{2}{3}\\\\\\frac{2}{3}\\end{matrix}\\right]\\right]$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m1=[Matrix([-2,1,0]), Matrix([2,0,1]), Matrix([-1,-2,2])]\n",
    "out(GramSchmidt(m1,true))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sin^{2}{\\left(x \\right)}}{2}$"
      ],
      "text/plain": [
       "sin(x)**2/2"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "integrate(sin(x)*cos(x),(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.00483264721675318$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.0257839721254356$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def cha(x,y):\n",
    " return (x-y)/x\n",
    "a=5.430*10**(-4)\n",
    "b=3.10*10**(-2)/(4*3.14**2)\n",
    "t=1.677**2\n",
    "out(cha(1.6761,1.6680))\n",
    "out(cha(1.435,1.398))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0001397696863970142"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.932**2*b-a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0015513227999999998"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1/10)*1.200*(11.37/100)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0014904255497180414"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b*(1.377)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "61"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "551-490"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03868471953578326"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cha(1.551,1.491)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0041334108333333335"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1/12)*0.1333*(61/100)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.004285644828390604"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b*(2.335)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "153"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "286-133"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.035697620158656"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cha(4.286,4.133)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "j=0.87/10000/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "m=0.71230\n",
    "D=10.003\n",
    "d=9.391\n",
    "x=(1/8)*m*(D**2+d**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4350102168683332"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m=0.17621\n",
    "D=6.941\n",
    "d=7.039\n",
    "(1/12)*m*(D**2+d**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 5=0.0054185$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 10=0.009014$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 15=0.0150065$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 20=0.023396$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 25=0.0341825$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0.005418500000000001"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=4.133/1000+0.87/10000\n",
    "def u(x):\n",
    "    return a+2*0.2397*(x/100)**2\n",
    "out(u(5),'5=',u(10),'10=')\n",
    "out(u(15),'15=',u(20),'20=')\n",
    "out(u(25),'25=')\n",
    "u(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.005637201407765022"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b*2.678**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0031931878658860735"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cha(5.637,5.619)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "javascript:JsMod('',700,500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Invalid limits given: (16.761388618375005,)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32mC:\\Users\\ADMINI~1\\AppData\\Local\\Temp/ipykernel_18368/962095301.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m#integrate((-2-2*x)/(1+x**2),(x))\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;31m#integrate((x),(x))\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mintegrate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlog\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32me:\\RMlaboratory\\SoftWare\\Anaconda\\1\\lib\\site-packages\\sympy\\integrals\\integrals.py\u001b[0m in \u001b[0;36mintegrate\u001b[1;34m(meijerg, conds, risch, heurisch, manual, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1547\u001b[0m         \u001b[1;34m'manual'\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mmanual\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1548\u001b[0m         }\n\u001b[1;32m-> 1549\u001b[1;33m     \u001b[0mintegral\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mIntegral\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1550\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1551\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mintegral\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mIntegral\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32me:\\RMlaboratory\\SoftWare\\Anaconda\\1\\lib\\site-packages\\sympy\\integrals\\integrals.py\u001b[0m in \u001b[0;36m__new__\u001b[1;34m(cls, function, *symbols, **assumptions)\u001b[0m\n\u001b[0;32m     89\u001b[0m                 useinstead=\"the as_expr or integrate methods of Poly\").warn()\n\u001b[0;32m     90\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 91\u001b[1;33m         \u001b[0mobj\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mAddWithLimits\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__new__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunction\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0msymbols\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0massumptions\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     92\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mobj\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     93\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32me:\\RMlaboratory\\SoftWare\\Anaconda\\1\\lib\\site-packages\\sympy\\concrete\\expr_with_limits.py\u001b[0m in \u001b[0;36m__new__\u001b[1;34m(cls, function, *symbols, **assumptions)\u001b[0m\n\u001b[0;32m    496\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    497\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m__new__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunction\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0msymbols\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0massumptions\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 498\u001b[1;33m         \u001b[0mpre\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_common_new\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunction\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0msymbols\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0massumptions\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    499\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpre\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mis\u001b[0m \u001b[0mtuple\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    500\u001b[0m             \u001b[0mfunction\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlimits\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morientation\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpre\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32me:\\RMlaboratory\\SoftWare\\Anaconda\\1\\lib\\site-packages\\sympy\\concrete\\expr_with_limits.py\u001b[0m in \u001b[0;36m_common_new\u001b[1;34m(cls, function, *symbols, **assumptions)\u001b[0m\n\u001b[0;32m     46\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     47\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0msymbols\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 48\u001b[1;33m         \u001b[0mlimits\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morientation\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_process_limits\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0msymbols\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     49\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mli\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlimits\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     50\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mli\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m4\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32me:\\RMlaboratory\\SoftWare\\Anaconda\\1\\lib\\site-packages\\sympy\\concrete\\expr_with_limits.py\u001b[0m in \u001b[0;36m_process_limits\u001b[1;34m(*symbols)\u001b[0m\n\u001b[0;32m    154\u001b[0m                         \u001b[1;32mcontinue\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    155\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 156\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'Invalid limits given: %s'\u001b[0m \u001b[1;33m%\u001b[0m \u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msymbols\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    157\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    158\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mlimits\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0morientation\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: Invalid limits given: (16.761388618375005,)"
     ]
    }
   ],
   "source": [
    "#integrate((-2-2*x)/(1+x**2),(x))\n",
    "#integrate((x),(x))\n",
    "integrate(log(x), x)"
   ]
  }
 ],
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